Impact of media coverage on the transmission dynamics of TB with vaccines and treatment

Tuberculosis (TB) is one of the deadly infectious diseases affecting millions of individuals throughout the world. The main objective of this study is to investigate the impact of media coverage on the transmission dynamics of TB with vaccine and treatment strategy using mathematical model analysis. In the qualitative analysis of the proposed model we proved the existence, uniqueness, positivity, and boundedness of the model solutions, investigated both the disease-free and endemic equilibrium points, computed the basic and effective reproduction numbers using next generation matrix approach, analyzed the stability analysis of the equilibrium points, the backward bifurcation using the Castillo-Chavez and Song theorem and we re-formulated the corresponding optimal control problem and analyzed by applying the Pontryagin's Minimum Principle. In the model quantitative (numerical) analysis part, we performed the model parameters sensitivity analysis and carried out numerical simulation to verify the qualitative analysis results. The findings of the study indicate that if the reproduction number is less than one, the solution converges to the disease-free state, signifying the asymptotic stability of the TB-free steady state. Moreover, the existence of a backward bifurcation shows that the disease-free equilibrium coexists with one or more endemic equilibria, even when the basic reproduction number is less than 1. Furthermore, it is found that as media efficacy increases, the disease infection rate decreases, which consequently leads to an increase in prevention and treatment control strategies.